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I am unable to determine what the chord you describe is. I would guess that C-Eb-Gb-B, despite the spelling, is not classified as a seventh chord, and maybe considered enharmonic spelling of another chord. Alternately, you could consider it a diminished chord with an added tone (the major seventh),
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pair of members of the domain is related, is a transitive relation that is weaker than (i.e. that includes) T, and (2) the set of all such relations is closed under intersection, so the intersection of all such relations is another such relation; that intersection is therefore the smallest one.
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How does one determine if a tone is a part of a chord if one does not already know? It depends, obviously, on context. A Bb played during a C major chord (CEG) does not necessarily turn that major chord into a seventh chord. A nonchord tone always resolves, while a chord tone does not (see
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The chord C-Eb-Gb-B can be called a Cmi(ma7b5) chord in popular music. In common practice period theory it would be theoretically described as a "diminished-major chord," but because it uses thirds other than the M3 and m3, the chord is not found in the standard repertoire.
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Is there an algorithm, that, given a transitive relation T, will return the smallest relation R such that the transitive closure of R is T? Is there such a smallest relation? I'm looking for such an algorithm, and this seems the most logical place to find a link to it.
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a chord tone. Given a (seventh) chord with the four notes C-E-G-Bb, the Bb is a chord tone and
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There is indeed a smallest one. To see that, consider that (1) the relation whereby
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a part of a chord. Thus, in a seventh chord, a seventh is not a nonchord tone, it
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My best guess right now is a major chord with an added (minor) ninth, B-D#-F#-C.
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The principle aspect of a nonchord tone is that it is
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